Support for non-commuting fieldsv1.3

1 files changed, 28 insertions, 1 deletions

diff --git a/man/kondo_preprocess.1 b/man/kondo_preprocess.1
index 5ec1399..e6e5c59 100644
--- a/man/kondo_preprocess.1
+++ b/man/kondo_preprocess.1
@@ -1,5 +1,5 @@
 .Dd $Mdocdate: April 14 2015 $
-.Dt kondo_preprocess 1.2.1
+.Dt kondo_preprocess 1.3
 .Os
 .Sh NAME
 .Nm kondo_preprocess
@@ -94,6 +94,30 @@ defines external fields for A and B, denoted by a and b. They can be used as fie
 .D1 <axb.h>
 .Pp
 .It
+Scalar products of A's and B's may also be specified using the '<#.#>' syntax:
+.D1 <An.An>
+.D1 <Bn.Bn>
+.D1 <An.Bn>
+.D1 <An.h>
+.D1 <Bn.h>
+.Pp
+The difference between '[f #.#]' and '<#.#>' is that the former corresponds to a '#!symbols' entry whereas the latter is replaced by its corresponding polynomial when
+.Nm
+reads it (see
+.Sx meankondo Ns (1)).
+.Pp
+.It
+A vector 't=(t1,t2,t3)' of Pauli matrices (satisfying the Pauli commutation relations [ti,tj]=\\delta_{i,j}1+\\epsilon_{i,j,k}tk) is introduced as a non-commuting object. It can be used in scalar producs:
+.D1 <An.t>
+.D1 <Bn.t>
+.D1 <t.h>
+.D1 <a.t>
+.D1 <b.t>
+.Pp
+Note that the '<#,#>' must be used since these scalar products do not commute whereas '#!symbols' entries must commute (see
+.Sx meankondo Ns (1)).
+.Pp
+.It
 Furthermore, in order to simplify writing products of polynomials over each box index, if the polynomial contains a '%', then
 .Nm
 multiplies the polynomial by itself as many times as there are boxes (2^dimension times), replacing '%' with the appropriate box index. For example, if dimension=1
@@ -118,6 +142,9 @@ in which the polynomial can use the fields
 .D1 <a.h>
 .D1 <b.h>
 .D1 <axb.h>
+.D1 <t.h>
+.D1 <a.t>
+.D1 <b.t>
 defined above.
 .Pp
 Example: